1. Field of the Invention
The present invention relates to carrier phase and frequency detection in a receiver of a digital communications system.
2. Description of the Related Art
In many digital communications systems, a source generates digital information for transmission to multiple destination receivers. A transmitter processes the digital information into an encoded (e.g., error-correction encoded) and/or packetized stream of data. The stream of data is then divided into discrete blocks. Each of the blocks is mapped onto a corresponding one of a sequence of code or symbol values (“symbols”) chosen from a pre-defined alphabet A, and generated with a period TS, sometimes referred to as the “baud” period. Symbols may be modulated by an analog, e.g., radio frequency (RF), carrier, in amplitude, phase, and/or frequency prior to physical transmission through the communication medium. Many methods of mapping exist and are well known in the art, and these pre-defined alphabets are generated based on certain criteria. For example, data may be mapped into symbols of a complex data stream as pairs of in-phase (I) and quadrature phase (Q) component values that are subsequently modulated with an RF carrier.
A receiver performs several functions to demodulate and decode a received signal. Receiver functions include, for example, tuning and RF demodulation of the received signal to an intermediate frequency (IF) signal, synchronization with the RF carrier, equalization, symbol detection, and decoding.
FIG. 1 shows a typical prior art communication system 100 that may be employed for transmission and reception of digital television signals. Communication system 100 comprises transmitter 101 transferring signals through transmission medium 102 to receiver 103. Transmitter 101 comprises digital encoding system 111, premodulator/pulse shaper 112, radio frequency (RF) upconverter 113, carrier oscillator 115, and transmit antenna 114. Transmitter 101 receives user data from information source 110 (such as video, audio, and/or computer files) coupled to digital encoding system 111. Digital encoding system 111 may provide analog-to-digital (A/D) conversion, error-correction encoding, and/or bit-to-symbol mapping to generate a sequence of symbols selected from a predetermined alphabet. For example, data may be mapped into a complex-valued signal stream with pairs of in-phase (I) and quadrature phase (Q) components. Digital encoding system 111 provides the symbols to pre-modulator/pulse shaper 112. Pre-modulator/pulse shaper 112 modifies the symbols for the particular type of modulation, and may include a filter for pulse shaping of the symbols. The signal generated by pulse shaper 112 is provided to RF upconverter 113 which i) uses the signal to modulate a complex radio frequency (RF) carrier provided by carrier oscillator 115, and ii) amplifies and filters the signal. The modulated and amplified RF carrier is then emitted into the transmission medium 102 as an RF signal via transmit antenna 114.
Various modulation techniques, such as quadrature amplitude modulation (QAM), phase-shift keyed (PSK) modulation, or vestigial sideband (VSB) modulation are known in the art of communications to modulate the carrier. For example, modulation formats such as VSB are common formats used for transmission of digital television signals in accordance with, for example, the ATSC standard for digital television, “ATSC Digital Television Standard,” Doc. A/53, September 1995.
For these modulation techniques, a quadrature oscillator may be employed with a complex RF upconverter to form a modulator. The I signal component modulates the cosine component generated by the oscillator and the Q signal component modulates the sine component of the oscillator. VSB modulation is a form of single-sideband modulation in which the redundant sideband of a real-valued signal is removed in full by filtering, except for a small vestige of the sideband. For complex VSB modulation, a complex signal is formed with the Q component being the Hilbert transform of the I component (however, the Q-component thus contains no additional user information).
FIG. 2 shows complex VSB modulation implemented by premodulator/pulse shaper 112, carrier oscillator 115, and RF upconverter 113 of transmitter 101 in FIG. 1. The signal from digital encoding system 111 is split into two paths: an upper path and a lower path. The signal in the upper path is filtered with Hilbert filter 201 and shifted in phase by 90° with multiplier 204, creating the Q (imaginary) component of the VSB signal. The signal in the lower path is applied to delay 202, creating a delayed version of the lower signal corresponding to the I (real) component of the VSB signal. The signals from the upper and lower paths are combined in adder 205 to form the complex VSB signal. The complex VSB signal excites pulse shaper 203 to generate pulses having a shape optimized for detection at the receiver. Up-converter 113 then up-converts the output signal of pulse shaper 203 to the RF carrier frequency with a complex RF modulator using the complex carrier generated by oscillator 115.
The modulated carrier signal transmitted through the medium 102 (which may be, e.g., wire, optical fiber, atmosphere, space, etc.) comprises a series of analog pulses, each analog pulse being amplitude and/or phase modulated by a corresponding symbol in the sequence. The pulse shape used typically extends many symbol periods in time. This introduces the possibility of adjacent pulses corrupting each other, a phenomenon known as inter-symbol interference (ISI).
Returning to FIG. 1, receiver 103 includes antenna 120 receiving the signal from the medium 102, complex demodulator and sampler 121, timing recovery module 122, equalizer 123, and carrier recovery module 124. Carrier recovery module 124 includes reference generator 126 and phase detector 125. Complex demodulator and sampler 121 translates the received signal from RF to intermediate frequency (IF), and performs complex demodulation of the received signal at IF to near passband employing the locally generated reference for the carrier signal. Complex demodulator and sampler 121 also samples the signal based on an estimate of the symbol period. Timing recovery module 122 estimates the symbol timing period TS, and this estimate may be fed back to complex demodulator and sampler 121 to adjust the sampling rate (e.g., via a sampling phase error). Timing recovery thus synchronizes sampling instances to the top-dead-center of the pulse shapes, and then tracks variations in the detected period and phase of TS.
Equalizer 123 applies equalization to the received samples, e.g. to correct for ISI, and may generate a cost error term used by timing recovery module 122 to adjust its estimate of the symbol timing period TS. Carrier recovery module 124 generates estimates for the difference in frequency and phase (collectively referred to as angle θ) of the carrier used to modulate the symbols and the locally generated reference used for demodulation. From the estimate of angle θ, carrier recovery module 124 adjusts the reference for complex demodulation to adjust the received signal to precise baseband. A detector 150, typically implemented with a slicer, examines each sample to generate either a soft or hard decision for the symbol that corresponds to the sample. After symbol detection, a decoder 151 reconstructs the transmitted data from the symbol sequence.
Many methods exist in the art for achieving synchronization of sample timing and/or carrier recovery. One method uses a separate pilot tone or preamble pattern in phase with the modulation process that is transmitted in addition to the information-bearing signal. The receiver derives synchronization measures from the separately transmitted information e.g., from the pilot tone. However, including a separate signal for synchronization reduces channel throughput (and uses both extra power and bandwidth) for pilot tone transmission and reception. Consequently, many applications use blind recovery techniques in which information for synchronization is derived from the received signal itself without the aid of side information, such as a pilot tone.
A receiver generally requires accurate knowledge of the received carrier signal's frequency and the carrier signal's phase offset (i.e., angle θ). Estimates of carrier frequency and phase offset are required to properly recover I and Q components of a passband or near-baseband signal and adjust the received signal to precise baseband for symbol detection. The estimation of carrier frequency and phase may be generated using samples obtained prior to equalization by equalizer 123, or equalized samples from equalizer 123.
A two-step procedure is often used in the prior art to accurately estimate the carrier frequency and phase offset at a given moment. The first step derives a coarse estimate of the frequency and phase offset, which reference generator 126 may generate directly from the samples. The second step derives a fine (i.e., an adaptive) estimate, and a phase tracking loop is generally employed including reference generator 126 and phase detector 125. The fine estimate tracks the phase jitter introduced into the received signal by 1) time-varying channel impairments and 2) phase noise introduced by low-cost tuner oscillators. Carrier estimation may be performed in discrete time, in continuous time, or in a combination of both discrete and continuous time.
The carrier tracking loop may use an estimated error as a control signal to the reference generator to minimize rotation between I and Q components of a locally generated estimate of the carrier signal (“reference”) and the received carrier signal. Alternatively, the estimated error may be processed to generate the error angle θ that is then used to de-rotate the demodulated signal. Phase detector 125 generates the measure (i.e., the error angle θ) between the reference and received carrier signal. The reference may be generated from a separate synchronization signal at the transmitter (termed “trained estimation”) or derived from the information signal itself (termed “blind estimation”). Trained estimation may be based on a continuous wave, such as a pure tone signal or a pseudo-random (PR) sequence of digital symbols, generated by the transmitter. For systems using blind estimation, the reference is not known to the receiver, and two typical techniques employed in the prior art are “power of N” and “decision directed” carrier recovery.
In power-of-N carrier recovery, the received signal is raised to the power N to create a strong spectral line at frequency 2πNfc, where N is positive and fc is the carrier frequency. The phase detector compares the phase of the signal raised to the power N to an initial estimated phase. The output (error) signal of the phase detector is loop filtered and applied to a voltage-controlled oscillator (VCO) with natural frequency 2πNfc. The output of the VCO corresponds to the estimated phase of the transmitted signal. The estimated offset is fed back to the phase detector and compared to the signal raised to the power N. The procedure is repeated until the error signal at the output of the phase detector is minimized. Power-of-N carrier recovery generally produces a noisy estimate of the carrier phase and frequency.
Decision-directed carrier recovery employs a phase detector that measures the angle θ between the received and (estimated) reference I and Q components that correspond to a nearest predefined symbol or “alphabet” member. Since each transmitted character is formed from known I and Q component values in amplitude and phase, the reference I and Q components are derived from the estimate (receiver's guess) of which symbol is received and under study. The output of the phase detector is coupled to a loop filter that controls the VCO generating the reference I and Q components. The output of the VCO is fed back to the phase detector to complete the phase tracking loop. Decision-directed carrier recovery is typically employed when the overall system Signal-to-Noise Ratio (SNR) is high.
Trained estimation is similar to blind estimation, except that the receiver uses the received reference to reduce error from estimation of the reference. For example, in carrier estimation based on a pilot tone, the estimate is derived in a manner similar to that of the power-of-N blind carrier estimate, but a pure tone signal of arbitrary frequency sent by the transmitter and known at the receiver aids in carrier estimation. For the ATSC standard for broadcast of digital television in the U.S., the transmitter embeds a single pilot tone at the band edge of the data spectrum. Mean square error estimation is comparable to the decision-directed blind estimation, but the angle between the components is computed by minimizing squared Euclidean distance between I and Q components of an estimated symbol sequence and a sequence generated by the transmitter (i.e., the training reference signal).
A receiver also generally applies equalization to the sample sequence prior to forming hard decisions for symbols. Equalization is used to suppress the effects of ISI, caused by phenomena such as i) residual timing error, ii) pulse shape/multipath distortion from the propagation channel, and/or iii) approximation of the ideal transmit and receive filters for ease of implementation. Adaptive equalizers may also use blind recovery techniques to derive tap coefficients for the equalizer filters.
One such blind cost criterion employed for equalization is the constant modulus (CM) criterion. The stochastic gradient descent of the CM criterion is known as the Constant Modulus Algorithm (CMA). The CMA algorithm is described in an article by D. N. Godard entitled “Self-Recovering Equalization in Two-Dimensional Data Communication Systems,” IEEE Transactions on Communications, vol. 28, no. 11, pp. 1867–1875, October 1980, which is incorporated herein by reference. The CM criterion and CMA algorithm were further developed to de-couple equalization and carrier recovery functions in a receiver. Such use of the CM criterion and CMA algorithm for equalization is described in J. R. Treichler et al., “A New Approach to Multipath Correction of Constant Modulus Signals,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-31, no. 2, April 1993, which is incorporated herein by reference. Systems that use such CMA algorithm for adaptive equalization, such as that described in U.S. Pat. No. 5,872,815 to Strolle et al., do not employ the CM criterion for timing or carrier phase recovery.
The CM criterion penalizes the deviation of the dispersion of the magnitude squared of the received signal from a pre-calculated constant referred to as the “dispersion constant” or the “Godard radius.” FIGS. 3A and 3B illustrate that the constant modulus criterion is based on deviation from a “radius” about the origin of, for example, a source constellation. FIG. 3A shows a radius 301 of an 8-PSK (phase-shift keyed) constellation plotted for real (e.g., Re or I) and imaginary (e.g., Im or Q) components. In FIG. 3A, each point (symbol) lies on the circle defined by this radius (termed a constant modulus system), and the CM criterion penalizes distance of a received sample (e.g., sample 302) from this circle. Even though the constellation may rotate, the constellation remains on the circle, and so applying a CM criterion to this constellation does not penalize spatial rotation of the constellation due to residual carrier offset. FIG. 3B shows a 16-QAM (quadrature amplitude modulation) constellation plotted for real and imaginary components. In FIG. 3B, groups of points (symbols) lie on corresponding concentric circles 311, 312, and 313. The CM criterion determines a radius 314 of circle 315, which is not necessarily a radius of one of the concentric circles 311, 312, and 313 (termed non-constant modulus), as a “common” radial distance from the origin for the points of the constellation. As with the constellation of FIG. 3A, the CM criterion penalizes distance of a received sample (e.g., sample 303) from this circle 315.
The CM criterion defines a cost function JCM that may be expressed as given in equation (1):JCM=E[(ρ2−|yn(τ,g)|2)2]  (1)where E[●] denotes the expected value, ρ2 is the dispersion constant (Godard radius), yn(τ,g) is the discrete value that represents the sampled signal, τ represents the timing (sampling) phase, and g represents the equalizer taps introduced to suppress the ISI. The dispersion constant ρ2 is a quantity that can be determined from the type of modulation employed (e.g., QAM, BPSK, etc.). The dispersion constant ρ2 may be derived by calculation, by experiment, or by a combination of both for a particular implementation. For real-valued source, such as VSB, the CM criterion, and its stochastic gradient, may be modified by taking the real part of yn(τ,g) in equation (1). The modified CM criterion is referred to as the single-axis (SA) CM criterion, and is given in equation (2).JSA-CM=E[(ρ2−Re{yn(τ,g, θ)}2)2]  (2)where Re{●} denotes the real-part extraction.
Given a defined cost function, the gradient of the cost function may be derived. The stochastic gradient is an approximation of the true gradient that is calculated by taking the derivative of the cost function without taking the expected value. For example, the stochastic gradient of the single-axis (SA) CM criterion is known as the SA-CMA and is derived by taking the derivative of equation (2) with respect to the variable of interest. Once the derivative is calculated, an error term may be defined that tends to drive the stochastic gradient to a relative minimum. For timing recovery, derivation of such stochastic gradient is described in U.S. patent application Ser. No. 09/761,303, entitled “Blind Cost Criterion Timing Recovery,” filed on Jan. 17, 2001, by the inventors herein and is incorporated herein by reference.